INSIGHT | REVIEW ARTICLES PUBLISHED ONLINE: 20 DECEMBER 2016 | DOI: 10.1038/NMAT4676

Energy conversion approaches and materials for high-efficiency photovoltaics Martin A. Green* and Stephen P. Bremner

The past five years have seen significant cost reductions in photovoltaics and a correspondingly strong increase in uptake, with photovoltaics now positioned to provide one of the lowest-cost options for future electricity generation. What is becoming clear as the industry develops is that area-related costs, such as costs of encapsulation and field-installation, are increasingly important components of the total costs of photovoltaic electricity generation, with this trend expected to continue. Improved energy-conversion efficiency directly reduces such costs, with increased manufacturing volume likely to drive down the addi- tional costs associated with implementing higher efficiencies. This suggests the industry will evolve beyond the standard single-junction solar cells that currently dominate commercial production, where energy-conversion efficiencies are fundamen- tally constrained by Shockley–Queisser limits to practical values below 30%. This Review assesses the overall prospects for a range of approaches that can potentially exceed these limits, based on ultimate efficiency prospects, material requirements and developmental outlook.

1 eports of the first efficient silicon solar cells in 1954 stimu- open-circuit voltage VOC, the current–voltage curve and the limiting lated calculations of ultimate photovoltaic efficiency2,3 and its efficiency5. The limits for standard single-junction cells and the fac- Rdependence on the semiconductor bandgap (Eg). Calculating tors that influence these are described below. current-generation limits in a short-circuited cell is uncomplicated: each incident photon of energy above Eg is assumed to create one Shockley–Queisser limits. Figure 1b shows limits calculated versus carrier that flows in the external circuit (Fig. 1a). Assigning funda- cell bandgap (or, more correctly, the absorption threshold, which is mental limits to the open-circuit voltage (VOC) is more problematic. often smaller thanE g, when effects such as excitonic and phonon- Initial approaches estimated bounds2,3 using Shockley’s semicon- assisted absorption are considered). Also shown are the highest ductor p–n junction theory4, combined with optimistic extrapola- experimental results6, plotted versus energy absorption threshold. tions of relevant material properties. Since there is no unique way of determining this threshold, it was Shockley and Queisser5 found an elegant solution to this dif- chosen for the plotted data as the photon energy, where experi- ficulty. Noting solar cells must absorb sunlight strongly, they real- mental cell photon-to-electron external quantum efficiency, EQEpe, ized the optimal material properties would be related to those of increases to half-peak value at long wavelengths. ideal black bodies, at least for energies above Eg. Unbiased in the Two crystalline materials, Si and GaAs, have demonstrated effi- dark, good cells would receive and emit largely ambient temperature ciency above 25%, with assorted crystalline, polycrystalline and black-body radiation. Emitted photons of energy above Eg over- thin-film materials demonstrating efficiency clustered around the whelmingly originate from radiative recombination of electrons in 21–22% range. A gap follows to the 10–15% range, where several the semiconductor conduction band with valence-band holes, as other materials can be found. the strongest optical process at such energies. Photons generated Three loss categories cause experimental performance to fall in this way would have various fates, such as being reabsorbed or below SQ limits: (1) collection losses, including photon reflection totally-internally-reflected at surfaces, but the number emitted is or absorption in poorly responding cell regions; (2) non-radia- readily quantified by integrating the ambient temperature black- tive recombination occurring together with radiative, decreas- body photon spectrum above Eg. ing output voltages, particularly for poor-quality materials and With a voltage V across the cell (Fig. 1a), Shockley’s p–n junction interfaces; (3) electrical losses, including cell series- and shunt- theory4 shows that carrier concentration near the junction increases resistances. Losses (1) and (3) depend on cell-design specifics. exponentially with qV/kT (where k is Boltzmann’s constant, T is Loss (2) can be quantified for any experimental cell by calculat- absolute temperature and q is electronic charge, with kT/q, the ‘ther- ing its external radiative efficiency7 (ERE), which is defined as mal voltage’, equal to 26.69257 mV at 25 °C). Intuitively, Shockley the fraction of net recombination when the cell is open-circuited and Queisser realized that, for good cells, similar enhancements that is radiative. (This is closely related to the electron-to-photon throughout active volumes would correspondingly increase recom- EQE when measured as a light-emitting diode (LED)). Because bination rates. Hence, the number of photons emitted by good cells SQ theory assumes 100% ERE, ERE determines how closely an under voltage would be the above-bandgap thermal equilibrium experimental cell approaches the ideal. emission enhanced by this exponential factor. Figure 1c shows cell energy-conversion efficiency versus ERE for a range of photovoltaic materials. For crystalline III–V materials, Single-junction cells ERE can be as high as 32.3% for the record 28.8%-efficient GaAs Calculating Shockley–Queisser (SQ) limits follows simply from the cell. For silicon, ERE is lower (0.1–2.2%) and constrained to values above insight. For limiting performance, all cell recombination will well below 100%, as intrinsic non-radiative Auger recombination be radiative. The current that supports this recombination is equal is stronger than radiative recombination8,9. Spanning the silicon to q times the emitted photon-flux, thus allowing calculation of the ERE values are the polycrystalline chalcogenides, copper indium

Australian Centre for Advanced Photovoltaics, School of Photovoltaic and Renewable Energy Engineering, University of New South Wales, Sydney 2052, Australia. *e-mail: [email protected]

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REVIEW ARTICLES | INSIGHT NATURE MATERIALS DOI: 10.1038/NMAT4676

a b 45 Sunlight AM1.5D 46,200Ž 40 SQ concentration limits Light emission 35

30 AM1.5G c-GaAs c-Si 25 c-InP CIGS Perovskite 20 mc-Si CdTe c-GalnP E„ciency (%) CIS p 15 CZTSSe Dye Organic n 10 nc-Si a-Si I CZTS CGS 5 c-Ge Reflector V 0 0.4 0.8 1.2 1.6 2.0 2.4 Bandgap (eV) c d 30

Silicon GaAs 25 Di•use CdTe CIGS 20 Half-angle

θ 15 CdTe Perovskite a-Si e„ciency (%) OPV CZTS Energy conversion conversion Energy 10 Di•use Dye Module 5 Direct

0 1 2 –7 –6 –5 –4 –3 –2 –1 10 10 10 10 10 10 10 10 10 10 ERE (%)

Figure 1 | Light absorption and emission, SQ limits, experimental energy-conversion efficiencies, radiative efficiencies and sunlight incident angles. a, Light absorption and emission from a solar cell under load. b, SQ energy-conversion efficiency limits under global sunlight (AM1.5G) versus energy absorption threshold (solid line), highest experimental values for various materials (data points) and limits for direct AM1.5D sunlight conversion under maximal concentration of 46,200 suns (dashed line), all at a cell temperature of 25 °C. Limits for other concentration ratios lie roughly geometrically intermediate between the solid and dashed lines, such that the curve for a concentration of 215 suns would lie around halfway between the two. c, Energy- conversion efficiency versus ERE for various experimental cells.d , Angular effects in solar energy conversion, showing direct and diffuse solar components, minimum acceptance angle and ground reflection effects. Data taken from refs 6,7. gallium selenide (CIGS) and recently emerging perovskites. Next Ross13, extended by Würfel14, and recently discussed analytically15. come other chalcogenides, CdTe and CZTSS (Cu2ZnSnSySe4–y), The second refinement relates light emission from practical cells to followed by dye-sensitized amorphous silicon and organic pho- black-body emission16. In one of the semiconductor device field’s tovoltaic (OPV) cells. Organic LEDs have high values of electron- surprising reciprocal relationships, emission from an actual cell, to-photon EQE because they are designed differently to their OPV with some provisos, equals that from the black-body ideal at each 10 counterparts , with LED-like design perhaps explaining one out- wavelength and voltage, except multiplied by EQEpe at that wave- lier in Fig. 1c — an organic photovoltaic cell with modest conver- length when used as a solar cell16. (The same relationship also applies sion efficiency despite reasonable ERE. The other outlier, a CdTe to LEDs, although this is possibly not as well-known or exploited in cell with 21% efficiency despite low ERE, is explained by high-qual- that field.) ity processing, which gives a good fill-factor and photogenerated carrier collection. Concentrated sunlight. One way to exceed original SQ limits is to The original SQ theory has been extended by two refinements. focus sunlight. The current in a short-circuited cell increases lin-

One is to include stimulated emission, which allows accurate treat- early with photon flux, whereas VOC increases nearly logarithmi- ment of the relationship between cell VOC and Eg. The original the- cally, thus giving a superlinear increase in power. The concentrator 11 17 ory predicts VOC > Eg/q under some conditions (small Eg, strong acceptance half-angle θ (Fig. 1d) determines the maximum pos- 2 illumination and low T), with the refinement limitingV OC to Eg/q sible sunlight concentration (in air) of 1/sin θ. At its mean distance, for ideal black-body cells (not necessarily for other cells12). The the Sun subtends a half-angle of 0.2665° at the Earth’s surface12, extended stimulated-emission formulation was first mentioned by which corresponds to a maximum concentration of 46,200 suns.

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NATURE MATERIALS DOI: 10.1038/NMAT4676 INSIGHT | REVIEW ARTICLES

The dashed line in Fig. 1b shows the limiting efficiency when the both hemispheres, SQ limits decrease slightly due to the doubling of reference AM1.5D (air mass 1.5, direct illumination) spectrum is emission and the radiative recombination supporting it. However, concentrated by this factor. energy output can increase by as much as 20–30%, particularly with We note the potentially large gain in efficiency here, although high ground reflection26,27. some caution is needed. Only direct sunlight can be concentrated effectively and calculated efficiency relates only to this component, Temperature. Solar cell efficiency decreases with increasing temper- 14 with incident diffuse sunlight — a large component of terrestrial ature. At 0 K, calculating SQ limits simplifies because VOC = Eg/q. sunlight18 — simply neglected. Because standard photovoltaic refer- Performance decreases approximately linearly to the 25 °C values ence spectra19 are clear-sky spectra, 90% of sunlight in the stand- in Fig. 1b. In the field, solar modules normally heat to temperatures ard AM1.5G (air mass 1.5, global illumination) spectrum is direct. that reflect their nominal operating cell temperature28 — typically Converting this with more than 11% relatively higher efficiency 44 °C, the temperature reached in an open-circuit configuration would increase output. However, high air mass, cloudy, hazy or under 800 W m–2 illumination at an ambient temperature of 20 °C overcast conditions all increase the diffuse fraction, thus increas- and with 1 m s–1 wind. This temperature rise decreases output by ing this required margin. Additionally, optical and resistive losses 5–12%, depending on the technology28,29. are more significant under concentration. Concentrators must also Heat losses from modules occur by convection, often wind- track the Sun’s position, with this being optional in non-concentrat- assisted, and by radiative transfer to sky and ground28,29. As well as ing systems. On the plus side, concentration reduces the importance receiving sunlight from various directions (Fig. 1d), modules emit of cell costs by reducing cell area, thereby providing opportunities and receive thermal radiation from these directions, in addition to for the early introduction of advanced, high-efficiency concepts SQ luminescent radiation. Most incident radiation comes at shorter such as those discussed below. wavelengths — below 4 μm — whereas at longer wavelengths mod- It is worth noting that direct sunlight can be converted with high ule thermal radiation exceeds that received. efficiency while simultaneously exploiting diffuse light, as suggested A module with ideal thermal design strongly absorbs above- by Goetzberger, who described the use of a common scheme12 in bandgap photons while reflecting sub-bandgap photons over the which a Fresnel lens array focuses direct sunlight onto high-effi- wavelength band extending to 4 μm, in which more photons are ciency concentrator cells. However, the space between concentrator absorbed than emitted, with modules here ideally reflective for cells is filled with low-cost cells, which convert diffuse light (simi- all incident angles. An atmospheric window of 8–13 μm allows larly for direct light misdirected by lenses). heat-sinking to cold space30–32 rather than to ambient, so strong absorption and hence emission in this band is desirable. Even with Acceptance angle. Similar gains can be obtained without concen- hemispheric emission through a perfect window, only 133 W m–2 tration, in principle, by restricting cell acceptance angles so that can be dissipated this way at 20 °C, with experimental demonstra- cells convert light only from a limited directional range20,21. A non- tions reaching 40 W m–2 (ref. 30). concentrating Sun-tracking cell could absorb all direct sunlight if Sub-ambient module temperatures are therefore feasible only its acceptance half-angle θ equalled that subtended by the solar disc for ultrahigh conversion efficiencies, at the upper limits discussed (Fig. 1d), with large values of EQE within the associated cone. If below. Less efficient devices are constrained to operating temper- the cell reflected all light outside this cone, it would not emit at atures linked to sky, ambient and ground temperatures. The ideal such angles (EQE = 0). In principle, emission would be reduced by module fully absorbs above the bandgap, fully reflects at interme- sin2θ, with limiting efficiencies identical to the highest in Fig. 1b diate wavelengths extending to 4 μm, and fully absorbs at longer (dashed line). wavelengths32. Standard modules approximate this ideal because In this case, diffuse light also need not be wasted, as cell emission low-iron glass coversheets become absorbing beyond wavelengths is strongly concentrated near the absorption edge. Light outside the of 4 μm (ref. 33), although improvements such as the use of micro- acceptance cone could be accepted provided the associated energy metre-sized, pyramidal-texturing of top glass surfaces may help absorption threshold is around 300 meV higher, which is feasible in this regard32. Interestingly, these features have been used in because diffuse light is relatively stronger at blue wavelengths22. high-performance modules, but to improve reflection and angular Dielectric antireflection coatings become more reflective at longer response rather than thermal performance34. wavelengths because the incidence angle increases, which suggests possible practical implementations20,23. Multijunction cells Although the limiting efficiency is identical to that under concen- One early suggestion — the most practical to date — involved tration, non-radiative recombination becomes much more signifi- improving efficiency beyond SQ limits, even before these limits cant. Regardless of non-radiative recombination rates (hence ERE), were known, by steering different wavelength bands of sunlight to

concentration to 1,000 suns ideally increases VOC by around 180 mV cells of appropriate bandgap for efficient conversion. Two schemes (= (kT/q)ln(C)) at fixed cell temperature, with a concentration (or were originally suggested35, either using filters to direct different angular restriction) ratio of C = 1,000. However, if a smaller accept- wavelengths to appropriate cells (Fig. 2a), or, more elegantly, stack- ance angle is used to reduce light emission by a factor of 1,000, this ing cells on top of one another, arranged by bandgap to provide voltage gain occurs only for ideal cells where ERE = 1. For smaller automatic filtering (Fig. 2b). The first approach has been used effec- values of ERE, the gain becomes (kT/q)ln{C/[C – (C – 1)ERE]}, tively in concentrators36, whereas the second may be sufficiently which approaches zero as ERE → 0. Even for the highest experimen- low-cost to be suitable for ‘one-sun’, unconcentrated sunlight use, as

tal ERE to date (32.3%), VOC would increase by only 10 mV, thus stacking can be monolithic, with cells series-connected to produce restricting gains to <1% under favourable assumptions, with this simple two-terminal devices. restriction not always emphasized in the literature24,25. Early work extended the SQ approach to the analysis of such Benefits can also accrue from increasing — rather than decreas- schemes37,38. One important issue, particularly as radiative limits ing — acceptance angle. Substantial sunlight falls on the rear of a are approached, is the treatment of radiative coupling between cells solar panel (Fig. 1d), either as diffuse sunlight or sunlight reflected (Fig. 2b). Although coupling can reduce sensitivity to variations from clouds, ground or other posterior structures. For fixed arrays, in sunlight spectra, the highest efficiency occurs when coupling is direct sunlight strikes panel rears on summer mornings and/or suppressed39. Figure 2 shows the corresponding limiting efficiency evenings. If panel acceptance angle is increased to accommodate versus energy absorption threshold of the lowest-bandgap cell in a

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REVIEW ARTICLES | INSIGHT NATURE MATERIALS DOI: 10.1038/NMAT4676

a b c Spectrally sensitive mirrors Sunlight 80 Infinite J AM1.5D 46,200 70 AM1.5G concentration 60 6J 50 3J 4J D III–V 3J D III–V Sunlight 40 2J 3J III–V 2J D III–V 5J III–V

E ciency (%) 30 Decreasing cell bandgap cell Decreasing 2J GalnP/Si* 2J III/V 20 1J 3J a-Si/nc-Si/nc-Si 10 2J a-Si/nc-Si 0 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 Solar cells of dierent bandgaps Bandgap (lowermost cell; eV)

Figure 2 | Multiple-junction cells, efficiency limits and highest experimental results.a , Spectral splitting approach, in which filters are used to direct different wavelength bands in sunlight to appropriate cells.b , Stacked tandem cells, showing light transmission and radiative coupling. c, Limiting conversion efficiencies of various series-connected stacked tandem cells as a function of the energy absorption threshold of the lowermost cell and the number of cells in the stack (solid lines). Also shown (dashed line) is the limiting efficiency for a stack containing an infinite number of cells under maximal concentration (46,200 suns). Results for infinite cell numbers under other concentrations would be approximately geometrically intermediate between the upper AM1.5G and the dashed curve. Data points show the highest experimental efficiencies for different cell technologies under both unconcentrated (AM1.5G) and concentrated (AM1.5D) sunlight, with the number of junctions and cell materials also indicated. 3J, three-junction cells; D, concentrator cells under direct sunlight; *, mechanically stacked four-terminal device. All other devices are two-terminal monolithic devices. Data taken from ref. 6. series-connected stack. Solid lines show the case of AM1.5G illu- Sub-bandgap absorption mination, with a limiting efficiency of 68.0% for stacks that involve A significant loss in standard cells is the wastage of sub-bandgap essentially infinite cell numbers, for lowermost cell thresholds of photons. One early suggestion for tackling this issue was the use <0.5 eV. Stacks with finite cell numbers can approach this limit, as of mid-gap states to capture such photons in a two-step absorption cell numbers increase. process (Fig. 3a)51. In their original paper5, Shockley and Queisser Monolithic tandem cells have been most successfully imple- suggested that analysing this problem using the SQ approach would mented in the III–V material system, with record 38.8% efficiency show no benefits, with similar conclusions made in subsequent stud- measured under unconcentrated sunlight (AM1.5G) for a five- ies52. The proposal of a related multiple-absorption-threshold device junction device40 that involves cells fabricated on GaAs and InP — the multiple-quantum-well cell53 (Fig. 3b) — which involves car- wafers and then subsequently bonded together. The best two- and rier photogeneration in lower-bandgap quantum-well regions and three-junction results are 31.6% and 37.9%, respectively, again subsequent thermal escape to the higher-bandgap host material, using III–V semiconductors41,42. Another successful implementa- stimulated work that clarified the basic thermodynamics of the two- tion has been in the thin-film amorphous-silicon (a-Si) and related step absorption process. nanocrystalline-silicon (nc-Si) system. Although efficiencies Associated thermodynamic constraints were resolved by extend- are much lower in these systems than in III–V material devices ing SQ concepts to the related intermediate-band cell54 (Fig. 3c). The because of a more marginal material quality, they are appreciably corresponding device equivalent circuit for schemes of Fig. 3a–c is higher than related single-junction devices. An AM1.5G efficiency shown in Fig. 3d, where the rectangular circuit elements represent of 13.6% has been reported for a triple-junction a-Si/nc-Si/nc-Si SQ-type cells. cell43, compared with 10.2% and 11.8% for the best a-Si and nc-Si Under concentrated sunlight, the efficiency limit approaches that devices, respectively44,45. of a three-cell tandem (Fig. 3e), as the parallel connection of Fig. 3d Increasing sunlight concentration (or restricting cell acceptance is not unduly restrictive. Energy wastage by absorbing high-energy angle) increases efficiency limits, with the dashed line in Fig. 2c photons in excitations possible with lower-energy photons must showing the infinite cell limit under maximal AM1.5D concen- be avoided. Correlating the absorption strength for each excita- tration. A maximum of 86.0% is possible when the lowermost cell tion with its energy threshold or, alternatively, finite bandwidths for bandgap approaches zero. Best experimental results are 46.0% at a both valence and conduction bands, are two suggested strategies for concentration of 508 suns for a four-junction wafer-bonded cell46, avoiding such wastage12. with efficiencies of 44.4% and 34.1% for three- and two-junction The parallel connection becomes more restrictive under one-sun cells42,47, respectively, again all using III–V semiconductors. operation, as the combined voltage from elements C1 and C2 drops Considering likely photovoltaic evolutionary paths, it has been twice as rapidly with decreasing illumination as from element C1, argued48 that a key challenge is the search for a low-cost thin-film thereby inhibiting a good voltage match. Importantly, efficiency can cell that can be deposited onto silicon or other commercial cell tech- be improved if the defect level energy relaxes after occupation by an nologies to form high-efficiency tandem cells, with much present electron to a state that does not communicate radiatively with the interest in perovskite/silicon tandem cells. Even triple-junction band from which it originated (Fig. 3a), or, alternatively, if there is cells in this material system may be feasible, although substantial a ‘ratchet’ band with similar properties to which electrons can relax, improvements in perovskite cell stability are essential before prac- in the case of intermediate-band devices (Fig. 3e). Benefits can be tical application is possible. Unconfirmed efficiencies above 20% significant. For a silicon cell with ERE = 0.3%, introducing defects have been reported49,50, although poor stability is likely hindering with ERE = 1% for transitions between the defect and either band independent confirmation. Similarly, using tandem stacks to super- increases the calculated efficiency from 26.7% to 32.0% with defect charge other commercial technologies, such as CdTe and CIGS, relaxation, assuming appropriate photon use55. Without relaxa- would boost efficiency to levels that might eventually become man- tion, an optimally located defect with otherwise identical proper- datory to maintain competitiveness in the future. ties would reduce the efficiency to 18.4%, thus justifying earlier

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pessimism regarding impurity photovoltaics5,52. Unfortunately, no a c defects with the required properties have yet been demonstrated. CB CB hf2 For quantum-well cells (Fig. 3b), the conclusion is that funda- hf2 2 2 Relaxation mental improvements are only possible if carrier excitation from Mid-gap wells involves particles that are not in equilibrium with the lattice56. level Impurity band hf1 Examples are solar photons or hot phonons, which have higher 1Ĕ 1 hf1 effective temperature than the lattice. Even without such involve- VB VB ment, the quantum-well concept has proved to be useful because the additional well-region materials offer flexibility in bandgap b d and lattice-spacing control. Quantum-well cells that exploit these CB Thermal escape advantages briefly held the efficiency record for single-junction -con centrator cells57. hf C2 Absorption Intermediate band and impurity photovoltaic principles can be C1 50 Recombination extended to multiple bands or defect levels . The number of allowed VB transitions increases quickly, as do constraints on allowed energies, C3 thereby sometimes restricting improvements even in ideal cases58,59. Attempts to implement intermediate-band devices in III–V and other 60 material systems have not been particularly successful ; significant e challenges remain for this approach, despite large potential gains. 70 AM1.5D 60 Photon wavelength manipulation 46,200x AM1.5G (with relaxation) Because the mismatch between photon energy and cell bandgap is 50 a key contributor to relatively modest SQ limits, a generic approach AM1.5G 40 for improving efficiency is to manipulate sunlight prior to con- (no relaxation) version. Luminescent concentrators and photon up- and down- 30 SQ

converters are key examples, as is thermophotovoltaics, which we Eciency (%) limit AM1.5G discuss below as a thermal approach. 20 61,62 Figure 4a shows the principles of a luminescent concentrator . 10 Dye molecules or quantum dots impregnated into glass or plastic sheets absorb solar photons and subsequently re-emit them at lower 0 energies in a narrow energy range close to the absorption thresh- 0.5 1 1.5 2 2.5 3 Bandgap (eV) old, but in random directions. A reasonable fraction will be totally- internally-reflected on striking surfaces of the embedding sheet and, Figure 3 | Sub-bandgap absorption processes, equivalent circuit and through successive surface reflections, will be guided to the edges. limiting efficiencies.a , Excitation from the valence band (VB) to the Solar cells along these edges then convert the narrow-bandwidth conduction band (CB) through a mid-gap defect level, both without (left) light with high efficiency. and with (right) defect energy level relaxation. b, Quantum-well solar cell An appealing feature of luminescent concentrators is that they showing carrier generation by low-energy photons in quantum wells, with can concentrate both direct and diffuse sunlight. Analysing losses subsequent escape to the higher-bandgap host material. c, Solar cell in in practical systems can be complex, but high-level analysis of ideal- which an intermediate band is present, such as when impurities are present ized systems produces an interesting result63. If a spectrally sensitive in sufficient quantities to cause overlapping between isolated states. omnidirectional reflector — a ‘hot mirror’ — is placed along the d, Equivalent circuit that is common to sub-bandgap absorption approaches. top surface of the luminescent sheet so that all light below a certain The boxes indicate SQ-like cells, with box length representing the value energy threshold is reflected64 (with the rear surface covered by a of the cell’s energy absorption threshold. e, Limiting efficiency under standard reflector), the limiting efficiency equals the SQ limit, with unconcentrated AM1.5G sunlight with and without energy relaxation (solid E replaced by the top-surface reflection threshold63. g lines), achieved by relaxing to a ‘ratchet band’ in the case of intermediate- The expected good performance of a concentrator arises because band cells113. The dashed line shows results under maximally concentrated the limiting efficiency decreases only slowly as the ratio of cell area AM1.5D radiation, where relaxation makes no significant difference. to aperture area decreases, reaching more than 30% for geometric concentrations above 100 times. The situation is even better for cells with non-ideal properties. For a silicon cell with ERE = 0.24% and through a two-step process similar to excitations in impurity photo- a conventional efficiency limit of 25.7%, an only slightly lower effi- voltaic and intermediate-band cells. Instead of being collected, the ciency of 23.9% is calculated63 in an ideal fluorescent concentrator excited electrons relax to their ground state and thus emit a high- at a geometric concentration of around 200 times. energy photon that is absorbed upon re-entering the cell. A hot mirror is essential for such performance, although it is The equivalent circuit for a two-step rear up-converter is shown challenging to implement. Without a hot mirror efficiency falls rap- in Fig. 4c. Efficiency increases appreciably under one-sun opera- idly with increasing geometric concentration, even under ideal con- tion only if the intermediate state relaxes during the two-step ditions63. The most efficient experimental device lacks a hot mirror excitation. This allows SQ elements C3 and C4 (Fig. 4c) to drive and is only 7.1% efficient at a geometric concentration of 2.5 times65. element C2 strongly into forward bias, thereby increasing its emis- Efficiency can be improved, in principle, by stacking sheets with dif- sion. Efficiency limits under unconcentrated sunlight (Fig. 4d) ferent absorption thresholds62, but the luminescent approach does show substantial gains for all bandgaps, with a peak efficiency close not seem conducive to high efficiency; its benefits may lie instead in to that of optimal three-cell tandems (Fig. 2c), as the equivalent attractive aesthetics66. circuit suggests. A second spectrum-manipulation approach is photon up-con- The main experimental difficulty has been low radiative efficiency 67 version (Fig. 4b) . In this scheme, photons with energy below Eg for practical up-converters — generally well below 1%. One suggested reach the rear up-converter and excite electrons to a higher energy improvement68 is the use of semiconductor up-converters (Fig. 4e).

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REVIEW ARTICLES | INSIGHT NATURE MATERIALS DOI: 10.1038/NMAT4676 a e higher68. This approach may also eliminate current-mismatch losses Sunlight that result from the low Ge bandgap in present triple-junction tan- Cell Sunlight dem cells on Ge substrates36. Luminescent Down-conversion69, in contrast, exploits the excess energy of centres C1 high-energy photons. If a photon with energy more than 2Eg is GaInP C2 intercepted before absorption, it can ideally double its carrier- GaInP C3 generation potential by converting to two lower-energy photons. GaAs C4 A possible front-surface configuration is shown in Fig. 4f, with an Glass or plastic sheet Ge equivalent circuit in Fig. 4g. For cells with band-absorption charac- b f teristics (as is the case for some organic cells), rear-surface location Sunlight Sunlight is also feasible69. High-energy photons absorbed in element C2 generate sufficient voltage to drive elements C3 and C4 into forward bias, thus emitting Down- photons that are then absorbed by the main cell. Because the band- Solar cell converter Insulator Insulator gaps of elements C1, C3 and C4 are all similar, the scheme involves Up-converter Solar cell essentially two different bandgaps and has efficiencies comparable Reflector Reflector to those of two-cell tandems. The largest gains are obtained when the bandgap of C1 is small (Fig. 4d). c g Down-conversion quantum efficiencies above 100% have been demonstrated experimentally70,71 although challenges remain in applying this technique to photovoltaics. A semiconductor down- C3 C3 converter could be implemented using III–V devices in a manner C1 C2 C2 C1 similar to the up-converter of Fig. 4c, although only modest effi- Sunlight ciency gains are expected compared with single-junction devices. C4 C4 Even with quantum efficiencies below 100%, practical benefits can accrue. Organic encapsulants in standard modules generally need protection from ultraviolet radiation. Absorbing ultraviolet photons d 50 in glass coversheets and down-shifting could be a useful strategy in Combined Up-converter this regard, particularly for cells with a poor ultraviolet response70. up- and down- (with relaxation) conversion Because up- and down-conversion favour large and small band- 40 Down-converter gaps, respectively, there is benefit, in principle, in combining both for cells with mid-range bandgaps (Fig. 4d). 30 Up-converter (no relaxation) Multiple carriers per photon SQ 20 limit AM1.5G SQ limits assume each absorbed photon produces a single carrier E‚ciency (%) in the external circuit. Early semiconductor photodiodes demon- 72 10 strated multiple-carrier generation by using high-energy photons , which becomes energetically feasible once the photon energy 0 exceeds 2Eg. Multiplication occurs through impact-ionization 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2.0 2.2 2.4 (Fig. 5a), which prompted the early suggestion of this approach for Bandgap (eV) improving efficiency73. Analysis using SQ methodology produces interesting insights74. Figure 4 | Photon wavelength manipulation using luminescent If multiple electrons/photons are introduced as a generation pro- concentrators and photon up- and down-conversion. a, Luminescent cess, the inverse-recombination process — two electron–hole pairs concentrator containing quantum dots or dye molecules impregnated recombining to give a single photon — must also be included to into a glass or plastic sheet. Light is absorbed and re-emitted at a longer avoid thermodynamic inconsistencies. There has been much recent wavelength with high quantum efficiency, after which it can be collected interest in multiple-exciton generation (MEG) in quantum-confined by cells along the edge of the sheet. b, Photon up-conversion. Photons of cells75, although the high-level analysis remains unchanged. There is energy below the cell absorption threshold pass through the cell and are obviously a strong connection with down-conversion, which sug- absorbed in a rear up-converter, where two (or more) combine to produce a gests links to two-cell tandems. Similar benefits would also apply if single higher-energy photon that can be converted by the cell. c, Equivalent MEG were combined with up-conversion. circuit for the up-conversion process. d, Limiting efficiency for photon Ideally the quantum yield (number of electron–hole pairs per up- and down-conversion when combined under unconcentrated sunlight absorbed photon) would have the staircase property approached in (AM1.5G). Energy relaxation of the intermediate state is critical for high Fig. 5c for large values of the parameter P. P is formally defined — efficiency in this case, as indicated. A refractive index of 3.6 was assumed perhaps obscurely — as the ratio of energy loss from multiple-particle 61 for the down-converter calculations . e, Proposed implementation of rear generation (kMEG) to that from other processes (kcool) (Fig. 5b), at an up-converter using III–V cells60. f, Photon down-conversion. A single high- energy twice the threshold for multiple-particle generation. Simple energy photon is absorbed in a down-converter prior to incidence on the theory72 gives a square-law dependence of this ratio with energy above cell, resulting in the subsequent emission of two (or more) lower-energy this threshold, where the threshold energy equals (2 + 1/P)Eg. More photons. g, Equivalent circuit for the down-conversion process. modest experimental performance is seen than that given by the ideal staircase, although data are well characterized by finite P values. In this system, current in the GaInP top cell is boosted by emission Experimentally, P ranges from well below 1 for bulk materials from the underlying GaInP cell, which is driven by absorption in the to a peak of around 10 for PbSe nanorods76. Corresponding effi- two lowermost smaller-bandgap cells. Although the limiting effi- ciency limits under non-concentrated AM1.5G sunlight (Fig. 5d) ciency is close to that of a three-cell tandem, its spectral tolerance is show that P values above 10 are required for gains over SQ limits,

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a b c d 310 45 Confined P = 10,000 k P = 7.3 P = 1.5 40 P = 100 states kMEG cool 280 P = 100 P = 0.83 35 PbSe (QD) 250 P = 10,000 P = 10 LUMO 30 SQ limit Ge (bulk) 220 AM1.5G PbSe (QD) P = 0.42 25 P = 4 Sunlight 190 P = 1 P = 0 Si 20 160 PbSe (bulk)

E ciency (%) 15 (NR) hf HOMO Quantum yield (%) 130 PbS (bulk) 10 PbSe (bulk) 100 5 70 0 1 3 5 7 9 11 13 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4

Photon energy (Eg) Bandgap (eV)

Figure 5 | Schemes in which a single photon creates multiple photogenerated carriers. a, Impact ionization, as observed experimentally in most semiconductors at high photon energies. b, Multiple exciton generation as found in quantum dots, showing confined energy levels and competing energy- relaxation processes. HOMO, highest occupied molecular orbital; LUMO, lowest unoccupied molecular orbital. c, Plot of quantum yield (number of electron–hole pairs created per absorbed photon) as a function of normalized photon energy, for a range of materials, compared with theoretical curves based on the parameter P (determined by the relative values of the loss processes in panel b). Bulk semiconductors generally have P values less than 1, with PbSe nanorods showing the highest values of 7.3 (Si and Ge data from ref. 114; other data from ref. 75). d, Limiting energy-conversion efficiency as a function of energy absorption threshold for unconcentrated AM1.5G sunlight across various values of parameter P. A value of P > 10 is required to improve upon the SQ limits (P = 0). Panels b–d adapted from ref. 75, ACS.

with values over 100 needed for significant gains. Under concen- Solar thermal conversion. As noted, solar thermal conversion

tration, small bandgaps become optimal and, consequently, ther- involves using heat from a receiver heated to temperature TC to modynamic and limiting efficiencies approach those of the thermal drive a heat engine, where its performance is limited to the Carnot 12,77 78 devices below . A recent milestone demonstrated absolute efficiency (1 – TA/TC), where TA is the ambient temperature. The EQEpe above 100%, although still far below the requirements for ideal case can be modelled simply when sunlight is approximated worthwhile efficiency gains. as blackbody radiation characterized by a constant temperature TS under maximal concentration (46,200 suns). The conversion effi- Thermal and related approaches ciency limit in this case is: The earliest approaches for converting sunlight into useful work 4 4 involved using absorption as heat and subsequent conversion η = (1 – TC /TS )(1 – TA/TC) (1) using heat engines79 (Fig. 6a). The associated thermodynamics are straightforward, particularly under concentrated sunlight, as is The history and properties of this equation are discussed else- normally the case. However, the thermodynamics of several other where80. For a 6,000 K Sun and an ambient temperature of 300 K,

approaches are very similar, as already noted for multiple-carrier the optimal efficiency is 85.4% for TC = 2,544 K. This receiver tem- generation, but thermodynamic links also exist to infinite tandem perature is beyond the capability of the materials used in practical

cell stacks, thermophotovoltaics, thermionics and hot carrier cells, solar thermal systems, which are generally limited to TC < 1,100 K which we discuss below. and efficiencies below 70%, even under the most ideal conditions.

a b c 80 Geothermal organic Rankine Infinite tandem-cell 70 Cement organic Rankine 80 Sunlight limits AM1.5D Carnot limit ZT = 20 (unlikely) 60 (ZT infinite) Solar thermal Solar Brayton Nuclear Brayton 60 Receiver T 50 wideband absorber C and Rankine Solar thermal Coal Rankine 40 Solar stirling selective absorber 40 Carnot Nuclear Rankine SQ limits 30 ZT = 4 (ambitious) Eciency (%) engine Eciency (%) Solar Rankine AM1.5D ZT = 2 (plausible) 20 20 Thermionics ZT = 0.5 (available) 10 TA Thermoelectrics Thermophotovoltaics 0 0 300 500 700 900 1,100 1,300 1,500 1 10 100 1,000 10,000 Solar temperature (K) Concentration (suns)

Figure 6 | Solar thermal conversion and conversion efficiencies.a , Idealized solar thermal converter. b, Theoretical and experimental conversion

efficiencies for converting heat (from a source at the temperature indicated) to electricity, for a range of conversion approaches (sink temperatureT A is 300 K). c, Limiting efficiency as a function of sunlight concentration for solar thermal conversion, with and without a selectively absorbing receiver

(TS = 6,000 K; TA = 300 K), compared with that of an infinite tandem cell and SQ single-junction cell limits, both under concentrated AM1.5D radiation. The thermal limits apply to many of the approaches described in this Review, whereas the infinite tandem results represent upper limits for time- symmetric systems. Panel b adapted from ref. 81, Nature Publishing Group, and ref. 82, Annual Reviews.

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a b Thermophotovoltaics. Thermophotovoltaics is the photovol- Electrons taic approach most directly associated with thermal conversion Receiver Cathode Anode (Fig. 7a). Emission from the heated receiver is confined to a narrow Tc Filter bandwidth, through filtering for example, and directed to a cell. The combination of a narrowband filter and cell acts as an ideal Carnot Sunlight p n Sunlight converter12, thus giving the same limiting efficiencies as thermal approaches85. A passive receiver permits the use of materials with higher receiver temperatures, although experimental solar conver- sion efficiencies remain modest86,87, fundamentally due to difficulties associated with designing filters that have the required omnidirec- tional reflection over the large energy range in which transmission c d Sunlight is detrimental. Recent developments include increased interest in near-field Hot receiver radiative transfer88, thermophotonics89 and the closely related ‘endothermic conversion’90, in which the emitter is a heated LED Hole Holes Electrons contact or photoluminescent device. These approaches have inherently nar- p n V Absorber Electron row-bandwidth emission and can boost emission temperatures by contact I Cool exploiting carrier excitation, as discussed previously. Thermionics. In thermionics (Fig. 7b), thermal energy is converted Resonant to electricity by electrons released at a hot cathode, which are then tunnelling contact collected at a cooler anode. This sub-process is limited to the Carnot efficiency, giving an overall limiting performance identical to solar Figure 7 | Approaches that are thermodynamically related to solar thermal limits. Although thermionic converters have been investi- thermal conversion. a, Thermophotovoltaics, whereby a cell responds to gated for powering spacecraft, demonstrated solar conversion effi- narrowband optical emission from a solar-heated receiver. b, Thermionic ciencies are below 10% (ref. 91; Fig. 6b). conversion, whereby sunlight heats a cathode that emits electrons In the photoelectric effect — the cornerstone of Einstein’s Nobel collected at the cooler anode. c, Thermoelectric conversion, whereby a Prize — electrons are ejected from conductors by energetic photons. hot receiver produces of flow of carriers towards a cooler junction, thus Sensitive and rapid-response photoelectric photodetectors and pho- allowing current flow to be maintained.d , Hot-carrier solar cell, in which tomultipliers have been developed92, although interest for their use photogenerated carriers are extracted before relaxing to the absorber band in solar conversion has been modest. The combination of thermi- edges. To prevent mixing with cold carriers in the contact, energy-selective onics with photon-enhanced thermionic emission was recently contacting is required, as shown using resonant tunnelling contacts in suggested to have potential advantages when high-temperature combination with doped semiconductor contact regions. operation is required93.

Figure 6b shows experimental efficiencies for converting heat Thermoelectrics. Thermoelectric devices generate voltage when into electricity from a source at various temperatures, compared there is a temperature gradient across the junction between two with Carnot limits81,82. For solar conversion, Stirling engines have dissimilar conductors, with doped p- and n-type semiconduc- the highest experimental values for this stage, with overall solar-to- tors being the most effective combination (Fig. 7c). Both electrons electricity conversion efficiencies of 31.3% reported83 and less well- and holes migrate from the hot junction, which allows current to substantiated 34% claimed84. Brayton cycles potentially offer higher flow between the cold terminals. Despite recent improvements in efficiencies through increased operating temperatures. the dimensionless thermoelectric figure-of-merit, the ZT product, However, very high equivalent temperatures can also be which were stimulated by investigations into new materials with reached in ambient-temperature electronic systems owing to high Seebeck coefficients and low thermal but high electrical con- exponential increases in carrier excitation, which we noted when ductivities81,82, demonstrated solar conversion efficiencies remain discussing SQ limits. The effective emission temperature of elec- low, generally below 10%. As shown in Fig. 6c, much higher val- troluminescent light with energy E is not the device temperature ues of the ZT product are required to compete with traditional heat 81,82 Tdev, but rather Tdev/(1 – qV/E), which becomes high at large inter- engines . Thermodynamically, thermoelectrics has strong links to nal voltages, V. Consequently, equation (1) also applies to an infi- ‘hot carrier cells’, which we discuss below. nite stack of tandem cells under maximal concentration when all are operated, slightly non-optimally, at a fixed fraction ofE g/q, Hot carrier cells. The loss in excess energy from energetic photons to give fixed emission temperature12. In this case, operation at ideally can be avoided by storing this energy in photoexcited carrier an effective temperature of 2,544 K poses no thermal problems, populations94. This requires slowing the normally rapid relaxation of which is a fundamental advantage of photovoltaics over solar photogenerated carriers to the bandedge94–96. thermal approaches. One way to achieve this ideal is to select absorbers with favour- To convert unconcentrated sunlight efficiently, a solar thermal able properties for reducing electron-to-phonon energy transfer95. receiver must display energy-selective absorption to avoid excessive A second way is to create ‘phonon relaxation bottlenecks’ that slow radiation back to the Sun. It must strongly absorb high-energy solar optical phonon relaxation, thereby creating hot phonons96. Carrier photons, but strongly reflect those below a certain threshold to limit populations then equilibrate with these hot phonons, rather than thermal emission. Figure 6c shows the similar relationship for lim- with the ambient96. iting efficiency versus concentration ratio for an idealized thermal Because contacts must allow unrestricted bidirectional car- converter and an infinite tandem cell stack. Although many of the rier interchange for low contact resistance, hot carriers in the following approaches have limits identical to those of thermal con- absorber would be swamped by cooler contact carriers if inter- version, in experiments they often fall further below the limits seen change between them occurred over the large energy range typical for practical versus ideal heat engines (Fig. 6b). of normal cells. The solution is to allow interchange over a restricted

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a b c Incident light Domain DW Domain DW Domain

CB Cladding θ1 n1 Recombination Active d2 n2= n2 ik2 D d2 hf VB n Cladding θ1 1

P P P

Scattering layer

Figure 8 | Alternative high-efficiency approaches.a , Time-asymmetric system with cell emission occurring in a different direction from sunlight incidence, in this restricted acceptance angle implementation. Implementations for diffuse light pose additional challenges104. b, Absorption enhancement in nanogeometries. The device in this case consists of a nanostructured stack of alternating high-index non-absorbing ‘cladding’ material and low-index

‘active’ absorber (ni and ki are the real and imaginary parts of the refractive index for the different layers; di and D are layer thicknesses; θi is the angle of incidence onto the layers shown). c, Ferroelectric photovoltaic effect. Change in electric polarization direction P( ) between different domains induces band-bending across the domain well (DW). hf is the photon energy. Panel c adapted from ref. 115, Nature Publishing Group.

range97. Resonant tunnelling through quantum dots dispersed in For infinite tandem cells, the time-symmetric efficiency a thin dielectric layer between the contact and the absorber may limit under concentrated AM1.5D sunlight is 86.0%. The time- also provide a potential solution12 by restricting transport to nar- asymmetric limit is 92.8% at ambient temperature11 (25 °C), but row resonant energy ranges (Fig. 7d). Additional heavily doped approaches 100% at lower temperatures. The atmospheric window semiconductors interposed between the dielectric and metal con- may provide sufficient cooling power to allow the heat dissipated tact (Fig. 7d) can reinforce this selectivity98. A balance is needed in a cell of this performance (<72 W m–2) to be emitted radiatively between the losses that result from excessively wide energy windows into cold space. This would allow operation at temperatures below and the large contact resistances that result from excessively narrow ambient and thus further boost efficiency, although overall this is energy windows98. an unlikely scenario. One simple way of maintaining hot carriers is to heat the The use of light management105, such as plasmonics, has been absorber99. The problem then is preventing heat loss to the ambient, suggested as another way to achieve high efficiencies. Interesting which is also the case for thermoelectric devices, indicating some results include the reformulation of light-absorbing limits for thin similarities. Geometries similar to Fig. 7d have been suggested for films using optical densities of states106, which can be enhanced implementing both hot carrier cells and thermoelectric devices100. near interface boundaries (Fig. 8b)107. However, SQ limits already A range of other hot-carrier issues continue to receive theoreti- assume perfect light absorption; such approaches therefore do not cal attention. For example, if carriers are all extracted at the same provide paths to exceed SQ limits, but rather provide possibilities energy, does scattering allow repopulation of the associated states for approaching them more closely. quickly enough to maintain output current101? Interest in ferroelectric photovoltaics108 has been rekindled by Although theoretical challenges remain and experimental pro- the recent emergence of lead-halide perovskite cells109. Although the gress is limited102, the hot carrier cell remains conceptually attractive operating principles of these cells are unresolved, ferroelectrics offer as a long-term photovoltaic solution. The two-terminal configura- above-bandgap voltage output probably by the serial connection of tion minimizes interconnection complexity, and ultrathin, strongly subdomains (Fig. 8c). The efficiencies of such devices remain mod- absorbing and radiatively efficient cells are essential for reducing est, despite recent improvements108. material requirements. In addition, hot carrier cells have higher Other recent work combines the techniques described above. This limits than solar thermal conversion and do not require high physi- context includes combinations already mentioned, such as photoe- cal temperatures (subtle band engineering to combine conduction- lectric-enhanced thermionic emission93, optical hot carrier cells89,110 and valence-band temperatures at each carrier energy allows the and endothermic converters90, as well as up-converters combined ultimate infinite-tandem limit to be reached103). with either down-converters or MEG. Some combinations enhance the prospects for demonstrating practical improvements. Other approaches A key limitation — one usually overlooked — is that the SQ Overall assessment approach and developments apply to normal time-symmetric sys- The present terrestrial photovoltaic manufacturing industry is tems, although time symmetry is not an essential photovoltaic dominated by silicon cells, and the stranglehold of this technology device property. Time asymmetry may allow, for example, a cell to is tightening48. Small, decreasing market shares (<9% combined) absorb light while suppressing the emission that is key to the SQ are held by CdTe, CIGS and a-Si thin-film modules (including a-Si/ approach, thereby increasing voltages and efficiencies. nc-Si tandems). For commercial space and concentrator cells, the A more detailed study104 has shown that energy conservation situation is different owing to different economic trade-offs. In these forbids this asymmetry. The best possible result is for cells to emit applications, silicon has been displaced over the past two decades light in different directions from that received104. Emitted light is by higher-efficiency GaInP/GaInAs/Ge triple-junction cells, both then available for second-stage conversion, with emission from lattice-matched and metamorphic111. this stage available for third-stage conversion, and so on (Fig. 8a). Although concentrating photovoltaic cells provide early oppor- Advantages become more pronounced as the efficiency of a single tunities for introducing advanced photovoltaics, herein lays a stage increases. problem, albeit an agreeable one. The improvement rate of III–V

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REVIEW ARTICLES | INSIGHT NATURE MATERIALS DOI: 10.1038/NMAT4676 multijunction cells has been the strongest and most sustained of all Regardless of the path taken by industry, photovoltaics are now photovoltaic technologies6. Costs, although high, are already close assured to have a major role in the future supply of energy on Earth, to the requirements of large-scale applications, with further reduc- with increasing interest in high efficiencies as a way of reducing tions expected as manufacturing volumes increase. Without realis- system costs112. Exploiting materials and designs to achieve success- tic prospects for efficiencies over 50% and some compelling market ful photovoltaic implementations will continue to be an important advantages, prospects for other advanced concentrator approaches research area well into the future. seem to be extremely limited. Applications in Space may provide other opportunities, not with Received 15 February 2016; accepted 23 May 2016; the aim of replacing III–V multijunctions, but instead for use as published online 20 December 2016 thermal converters, through approaches such as thermionics, ther- moelectrics and thermophotovoltaics, with such interest contrib- References uting to recent development84. Ongoing development may lead to 1. Chapin, D. M., Fuller, C. S. & Pearson, G. L. A new silicon p–n junction other large-scale applications such as the conversion of automobile photocell for converting solar radiation into electrical power. J. Appl. Phys. waste heat, which has been identified as the most likely route for 25, 676–677 (1954). 81 2. Prince, M. B. Silicon solar energy converters. J. Appl. Phys. 26, 534–540 (1955). thermoelectrics to contribute to climate-change mitigation . 3. Loferski, J. J. 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